Bound states in 2D fermion systems of graphen

Abstract

Analytical solutions for the zero-energy modes of two-dimensional massless Dirac fermions confined within the one-dimensional Lorentz-like potential, which provides а reasonable fit for potential profiles of existing top-gated graphene structures is performed. On the basis of obtained hypergeometrical equations we have studied the conditions for formation of quantum bound states providing an one-dimensional fermion localization. А simple relations between the potential parameters and number of modes within the potential are established. Possibility of realization of the external controlled charge transport in the studied 2D system is considered.